1 . 已知列向量
在矩阵
对应的变换下得到列向量
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93de6bcd660ecb8b8502a99042b00166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170550d1ec3dbecf60d9c0e032fc07cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987580b054aa27bb03b38ffd2d57e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741b5d472dbf09afa69442f57d54780b.png)
您最近一年使用:0次
2020-05-09更新
|
108次组卷
|
2卷引用:2020届江苏省泰州市高三下学期调研测试数学试题
2 . 已知
,若矩阵
所对应的变换把直线
变换为自身,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467053b6d48f6cfa2bca632d3592e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87ce39e2b89d40e02d578db34ecdefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
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3 . 点
经矩阵
变换后得到点
在直线
上,且矩阵
不存在逆矩阵,求实数
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab85fdf66f4d2000456eaf620fc9bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86076e60d1727a012a0eab695dd6914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbb5f75f035bc58830b9df835287b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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4 . 若二阶矩阵
满足
.
(1)求二阶矩阵
;
(2)若曲线
在矩阵
对应的变换作用下得到曲线
,求曲线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65f9ef504dc62b0ce159dbe325fa061.png)
(1)求二阶矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428756f1088ce78ed97cbcea99775f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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5 . 已知矩阵
对应的变换将点
变换成
.
(1)求矩阵
的逆矩阵
;
(2)求矩阵
的特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f067e864f45017e81acd12bc50b2991d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9155c035829f22ae89aa06ba34a22ee7.png)
(1)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 已知矩阵
,矩阵B的逆矩阵
.
(1)求矩阵A的特征值及矩阵B.
(2)若先对曲线
实施矩阵A对应的变换,再作矩阵B对应的变换,试用一个矩阵来表示这两次变换,并求变换后的结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27808e342b2864b11b838ba7f95b632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08876f55ffc5c720564e8e0cba17ce66.png)
(1)求矩阵A的特征值及矩阵B.
(2)若先对曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
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